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A061112 a(n) is the minimum number of divisors for any composite between prime(n) and prime(n+1).

%I A061112 #17 Aug 11 2023 10:00:26
%S A061112 3,4,3,6,4,6,4,3,8,4,4,8,4,3,4,12,4,4,12,4,4,4,4,6,8,4,12,4,3,4,4,8,4,
%T A061112 12,4,4,4,3,4,18,4,14,4,12,4,4,4,12,8,4,20,4,4,4,4,16,4,4,8,3,4,4,16,
%U A061112 4,4,4,4,12,8,4,3,4,4,4,4,4,4,4,4,24,4,20,4,8,4,4,4,16,4,4,4,4,4,4,4,4
%N A061112 a(n) is the minimum number of divisors for any composite between prime(n) and prime(n+1).
%H A061112 Harry J. Smith, <a href="/A061112/b061112.txt">Table of n, a(n) for n = 2..1000</a>.
%F A061112 a(n) = Min_{c=prime(n)+1..prime(n+1)-1} tau(c) where tau(c) is the number of divisors of c.
%e A061112 prime(30)=113 is followed by 13 composites; their numbers of divisors are {8, 4, 6, 6, 4, 4, 16, 3, 4, 4, 6, 4, 12}. The smallest is 3, so a(30)=3. [corrected by _Jon E. Schoenfield_, Sep 20 2022]
%t A061112 Array[Min@ DivisorSigma[0, Range[#1 + 1, #2 - 1]] & @@ Prime[# + {0, 1}] &, 95, 2] (* _Michael De Vlieger_, Aug 10 2023 *)
%o A061112 (PARI) { n=-1; q=3; m=10^6; forprime (p=5, prime(1003), a=m; for (i=q + 1, p - 1, a=min(numdiv(i), a)); q=p; write("b061112.txt", n++, " ", a) ) } \\ _Harry J. Smith_, Jul 19 2009
%Y A061112 Cf. A000005, A061117.
%K A061112 nonn
%O A061112 2,1
%A A061112 _Labos Elemer_, May 29 2001